2026-08-12 –, Room 6
Macroeconomic debt cycles evolve over time through interacting growth, inflation, and fiscal pressures. This study compares India, Sri Lanka, and Argentina using Physics-Informed Neural Networks (PINNs) and Universal Differential Equations (UDEs) to model continuous economic dynamics. By embedding economic structure into neural differential systems, we evaluate their ability to reconstruct national macroeconomic trajectories under sparse annual data conditions.
This project investigates whether continuous-time scientific machine learning methods can better represent such evolving economic systems. Building on the idea of long-term debt cycles, the study moves beyond a single country setting to compare India, Sri Lanka, and Argentina. Three economies with distinct fiscal histories and crisis trajectories. By analyzing multiple countries, the research expands its horizon from local model fitting to cross-country structural comparison. The central question is not about which model predicts better, but how embedding economic structure into learning systems affects stability, interpretability, and long-term trajectory reconstruction.
The methodology is based on Physics-Informed Neural Networks (PINNs) and Universal Differential Equations (UDEs). Unlike purely data-driven neural models, these approaches integrate differential equation structures and domain constraints directly into the learning process. This allows the model to respect economic relationships such as debt-growth feedback and dynamic fiscal adjustments while still learning unknown components from data. The implementation is carried out in Julia, leveraging its high-performance scientific computing ecosystem.
In particular, the project utilizes the DifferentialEquations.jl suite for numerical ODE solving, DiffEqFlux.jl and SciMLSensitivity.jl for neural differential equation training and adjoint-based gradient computation, and NeuralPDE.jl for physics-informed learning. Optimization is handled using Optimization.jl with ADAM and second-order solvers, while data processing and evaluation rely on DataFrames.jl and Statistics. Julia’s amazing SciML framework enables tight coupling between symbolic differential equations and neural networks, allowing us to experiment with both structural constraints and hybrid modeling. Using annual macroeconomic indicators, the study evaluates how well these hybrid systems reconstruct historical trajectories under sparse sampling conditions.
By comparing performance across three countries, the research explores how structural constraints influence validity, error accumulation, and generalization. Ultimately, this project aims to bridge macroeconomic modeling and scientific machine learning, advancing a more disciplined and interpretable approach to modeling national economic dynamics.
Vrishank Sai Anand is a Grade 10 student at GEMS Modern Academy in the UAE, originally from India. He was recognized as an Azeem Scholar and has received academic distinctions as a subject topper in Digital Design, Physics, Mathematics, and History. His academic interests lie at the intersection of Scientific Machine Learning (SciML), artificial intelligence, and quantitative finance, where he explores how mathematical modeling and algorithms can be used to understand complex economic systems.
He programs primarily in Julia and Python, with hands-on experience in SciML frameworks, neural differential equations, and research-oriented model development. Alongside his technical work, he has experience in UI/UX design, Flask-based web development, and deployment of computational projects, reflecting his interest in building both theoretical and practical systems.
Vrishank care's strongly about collaboration, communication, and impact. Through his podcast, Beyond Tomorrow - Navigating Fontiers, his school Futures Club, and his literacy initiatives in India, he has seen how powerful it can be to share knowledge and bring people together around ideas. Vrishank has authored an essay in the Journal of Future Studies on the “Digital Divide,” examining how book access and reading initiatives can reduce educational inequities. He has also won awards in the NGFP Young Voices Challenge in 2024 and 2025 for projects related to SDG 16 and SDG 4.
Beyond academics, Vrishank is a goalkeeper for Elite Sports in the UAE and has represented his school at the UAE IB Nationals. As a captain, he values discipline, leadership, and resilience, qualities he carries into his academic pursuits. He also enjoys playing video games, which complement his interest in systems thinking and decision-making.